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LefSer for his general discussion of the differential equations of
dynamics and an attack on the problem of three bodies. The
last is usually considered the most important case of the n-body
problem, as the Earth, Moon, and Sun furnish an instance of the
case n  3. In his report to Mittag-Leffier, Weierstrass wrote,
'You may tell your Sovereign that this work cannot indeed be
considered as furnishing the complete solution of the question
proposed, but that it is nevertheless of such importance that its
publication will inaugurate a new era in the history of Celestial
Mechanics. The end which His Majesty had in view in opening
the competition may therefore be considered as having been
attained.' Not to be outdone by the King of Sweden, the
French Government followed up the prize by making Poincare
a Knight of the Legion of Honour - a much less expensive
acknowledgement of the young mathematician's genius than
the King's 2,500 crowns and gold medal.
As we have mentioned the problem of three bodies we may
BOW report one item from its fairly recent history; since the
time of Euler it has been considered one of the most difficult
problems in the whole range of mathematics. Stated mathe-
matically, the problem boils down to solving a system of nine
simultaneous differential equations (all linear, each of the
second order). Lagrange succeeded in reducing this system to a
simpler. As in the majority of physical problems, the solution
is not to be expected in finite terms; if a solution easists at all it
will be given by infinite series. The solution will 'exist* if these
series satisfy the equations (formally) and moreover converge
for certain values of the variables. The central difficulty is to
prove the convergence. Up till 1905 various special solutions
had been found, but the existence of anything that could be
called general had not been proved.
In 1906 and 1909 a considerable advance came from a rather
unexpected quarter - Finland, a country which sophisticated
Europeans even to-day consider barely civilized, especially for
its queer custom of paying its debts, and which few Americans
thought advanced beyond the Stone Age till Paavo Nurmi ran
the legs off the United States. Excepting only the rare case
when all three bodies collide simultaneously, Karl Frithiof